Intervalssuch

Intervalssuch is a term used in theoretical discussions to denote the collection of all intervals that satisfy a given predicate within a specified domain. The term is not standardized and appears mainly in mathematical expositions or informal notes where the focus is on how intervals relate to a selection criterion.

Formally, let I denote an interval, typically represented as [a, b] with a ≤ b, and let P(I) be a predicate that may depend on the endpoints or on external data. The intervalssuch set for P is the set { I | I is an interval in the domain and P(I) holds }. Examples: P(I) could require length(I) ≥ L, or that I intersects a fixed set S, or that I is fully contained in another interval J. The concept is agnostic to whether intervals are closed, open, or half-open.

Computation and representation: Evaluating P for intervals can be done symbolically or numerically. In practice, data structures such as interval trees, segment trees, or sweep-line algorithms are used to manipulate the intervalssuch and support operations like membership testing, intersection, and containment queries.

Applications: intervalssuch concepts appear in scheduling, temporal databases and constraint programming, where one needs to reason about ranges of time, resources, or measurements that meet certain criteria. The term itself is not widely standardized and is mostly encountered in didactic contexts or niche literature.

See also: interval arithmetic, interval trees, temporal databases, constraint programming, range searching.